As investigators were still unraveling the details surrounding the Orlando shooting, Trump delivered a speech suggesting that the shooter was born in Afghanistan and was a radical terrorist.

But in fact the gunman, Omar Mateen, was the child of Afghan immigrants and like Trump was born in New York City.

Trump also reiterated his desire to bar Muslims from entering the United States.

"This whole speech, with its nativism, its fearmongering, and especially its self-aggrandizing in the face of tragedy, feels like a new low," Colbert said. "It makes me long for the days when Trump was just bragging about the size of his penis."

Trump also said both President Barack Obama and Hillary Clinton, the presumptive 2016 Democratic presidential nominee, were unable to deal with radical terrorism effectively.

"They have put political correctness above common sense, above your safety, and above all else," Trump said. "I refuse to be politically correct."

To which Colbert commented: "Donald Trump refuses to be politically correct. And just to be safe, he refuses to be correct."

But the comment that got most people talking was when Trump told Fox News that there might be "something else going on" in Obama's approach to dealing with terrorism, seeming to imply something more sinister about the president.

So when Trump challenged others to make sense of his statements, Colbert took him up on his offer. The late-night host brought in a chalkboard to chart Trump's statements. The first time he did it, he ended up with a giant swastika. He erased that quickly and started all over again.